Question: Solve for $x$ and $y$ using elimination. ${-6x+y = -22}$ ${-5x-y = -33}$
We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Add the equations together. Notice that the terms $y$ and $-y$ cancel out. $-11x = -55$ $\dfrac{-11x}{{-11}} = \dfrac{-55}{{-11}}$ ${x = 5}$ Now that you know ${x = 5}$ , plug it back into $\thinspace {-6x+y = -22}\thinspace$ to find $y$ ${-6}{(5)}{ + y = -22}$ $-30+y = -22$ $-30{+30} + y = -22{+30}$ ${y = 8}$ You can also plug ${x = 5}$ into $\thinspace {-5x-y = -33}\thinspace$ and get the same answer for $y$ : ${-5}{(5)}{ - y = -33}$ ${y = 8}$